Pertanyaan

Bentuk sederhana dari ( 3 − 1 x 3 2 y − 5 8 2 2 x − 3 7 y 5 2 ) − 1 adalah ....

Bentuk sederhana dari $(\frac{2 ^{2} x ^{- \frac{7}{3}} y ^{\frac{2}{5}}}{3 ^{- 1} x ^{\frac{2}{3}} y ^{- \frac{8}{5}}})^{- 1}$ adalah ....

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Untuk menyederhanakan bentuk eksponen tersebut, kita harus paham sifat bilangan eksponen. Terutamasifat-sifat berikut: Sehingga bentuk sederhanya: Jadi, bentuk sederhana dari adalah .

Untuk menyederhanakan bentuk eksponen tersebut, kita harus paham sifat bilangan eksponen. Terutama sifat-sifat berikut:

Sehingga bentuk sederhanya:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 2 squared x to the power of negative 7 over 3 end exponent y to the power of 2 over 5 end exponent over denominator 3 to the power of negative 1 end exponent x to the power of 2 over 3 end exponent y to the power of negative 8 over 5 end exponent end fraction close parentheses to the power of negative 1 end exponent end cell equals cell fraction numerator 2 to the power of negative 2 end exponent x to the power of begin display style 7 over 3 end style end exponent y to the power of negative begin display style 2 over 5 end style end exponent over denominator 3 to the power of 1 x to the power of negative begin display style 2 over 3 end style end exponent y to the power of begin display style 8 over 5 end style end exponent end fraction end cell row blank equals cell open parentheses 2 to the power of negative 2 end exponent over 3 close parentheses open parentheses x to the power of 7 over 3 end exponent over x to the power of negative 2 over 3 end exponent close parentheses open parentheses y to the power of negative 2 over 5 end exponent over y to the power of 8 over 5 end exponent close parentheses end cell row blank equals cell open parentheses 1 third times 1 over 2 squared close parentheses open parentheses x to the power of 7 over 3 minus open parentheses negative 2 over 3 close parentheses end exponent close parentheses open parentheses y to the power of negative 2 over 5 minus 8 over 5 end exponent close parentheses end cell row blank equals cell 1 over 12 open parentheses x to the power of 9 over 3 end exponent close parentheses open parentheses y to the power of negative 10 over 5 end exponent close parentheses end cell row blank equals cell 1 over 12 open parentheses x cubed close parentheses open parentheses y to the power of negative 2 end exponent close parentheses end cell row blank equals cell 1 over 12 left parenthesis x cubed right parenthesis open parentheses 1 over y squared close parentheses end cell row blank equals cell fraction numerator x cubed over denominator 12 y squared end fraction end cell end table end style$

Jadi, bentuk sederhana dari $begin mathsize 14px style open parentheses fraction numerator 2 squared x to the power of negative 7 over 3 end exponent y to the power of 2 over 5 end exponent over denominator 3 to the power of negative 1 end exponent x to the power of 2 over 3 end exponent y to the power of negative 8 over 5 end exponent end fraction close parentheses to the power of negative 1 end exponent end style$ adalah $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x cubed over denominator 12 y squared end fraction end cell end table end style$ .